negations

Negation is the linguistic and logical operation of expressing denial, opposition, or falsity of a proposition. In formal logic, negation is a unary operator that inverts the truth value of a statement: if p is true, not p is false, and if p is false, not p is true. It also participates in more complex constructions through quantifiers and connectives.

In natural language, negation is realized with words such as not, no, never, and with prefixes like un-, in-, non-, as well as periphrastic forms. The placement of negation interacts with scope: negation may apply to the verb, to the tense, or to the entire clause, altering which subcomponents are denied. Some languages use negative concord, where multiple negative elements reinforce negation instead of cancelling it. For example, The cat is not on the mat. Nobody came. I did not see anyone.

In logic, negation is governed by laws such as double negation (not not p is equivalent to p) and De Morgan's laws, which distribute negation over conjunctions and disjunctions. Negation also interacts with quantifiers: negating exists yields for all not, and negating for all yields exists not. These relations shape truth conditions and inference.

Cross-linguistic variation includes analytic negation with separate negators versus synthetic or affixal negation, and the possibility of negation playing a role in polarity items and speech acts. The study of negation covers semantics, syntax, pragmatics, and historical development, including the evolution of negating words and periphrastic constructions across languages.